* The SEP has an article on Impossible Worlds. I'm skeptical of some of the HoP implications suggested at the beginning; but if you admit a possible worlds formalism there are excellent reasons to admit an impossible worlds formalism.

* The "Chicago Boyz" blog is having a roundtable on Xenophon's Anabasis. Xenophon, against the advice of Socrates, joined the Ten Thousand, an army of mercenaries, to fight for Cyrus the Younger against his brother Artaxerxes II. They won a key battle at Cunaxa, but Cyrus was killed in the fight, leaving the Greek mercenaries stranded in hostile territory. Xenophon is usually overshadowed by Plato, but all of Xenophon's works (including the historical ones) are philosophical works, expressing his own brand of Socratism.

* Michael at "The Smithy" recently had a series of posts on the Theoremata Scoti:

* Speaking of the oddities of Belgian borders, meet the Vennbahn, a no-longer-used railroad running through Germany that by a still-functioning provision of the Treaty of Versailles is entirely in Belgium.

Thursday, September 24, 2009

Highly skilled at deduction, the German mind is poorly endowed with common sense. It has a limitless confidence in the discursive method, whereas its confused intuition gives it only a weak assurance of the truth. It is consequently peculiarly vulnerable to slipping into skepticism. It has frequently and ponderously fallen into it; Kant vigorously pushed it there.

What is the Critique of Pure Reason? The longest, the most obscure, the most confused, the most pedantic commentary on these words of Pascal: "We have an impotence to prove which cannot be overcome by any dogmatism."

Wednesday, September 23, 2009

There are a great many myths about Pierre Duhem floating around. The most notable, I think, is that he advocates scientific anti-realism; an attribution which requires a very selective reading of Duhem, ignoring everything in Duhem's arguments that Duhem himself seemed to have considered most important. I won't argue that issue here. What I do want to do is say something about the claim that Duhem rejected the theory of relativity.

The best text for understanding Duhem's view on relativity is German Science. There have been many complaints about this book; for instance, it has been called an unfortunate piece of (World War I) war propaganda. What offends about the work are what are usually called its caricature of the 'German mind'. There's no doubt that the work presents us with something of a caricature; but a caricature is not a wholly inaccurate portrait. A caricature involves some distortion, but only for the purposes of bringing out particularly recognizable or distinctive points. And Duhem himself is quite clear that in talking about the 'German mind' he merely wants to indicate a tendency that arises from the way the Germans teach and learn science, not to make a universal statements about Germans. As he notes, there is no trace of the exclusively 'English mind' in Newton, and no trace of the exclusively 'German mind' in Gauss. His interest in the subject, actually is that it provides a useful context for investigating the mentality that is ideal for scientific work. The Germans just happen to be the concrete case that (he thinks) comes closest to a pure case of one element of this mentality.

We often tend to talk as if scientific progress were unilinear, as if all scientists had one type of mentality in their scientific work, one methodical approach. Duhem does not. Duhem has a Pascalian view of the human mind, which means he thinks there are two (major) kinds of mentality. The first is the esprit de finesse, the intuitive mind; the second is the esprit de géométrie, the geometrical mind. All human beings have both to some extent. A rare few have close to the perfect balance of both. Most of us, however, tip strongly to one side. Some of us are primarily intuitive, some primarily geometrical. There are several different sorts of both. For instance, one sort of intuitive mind (Duhem calls it the 'English mind') is heavily imaginative -- it relies on models, picture-thinking, metaphors. Another (the 'French mind' -- but Duhem is very clear that it is the French mind as it used to be, in the days of Pasteur or Ampère) is very formal; it eschews the messiness of models and pictures in favor of formal structures that lay things out neatly and clearly. No doubt there are other possible variants. The 'German mind', Duhem thinks, is geometrical.

Duhem insists that the healthy progress of science requires the active participation of both intuitive and geometrical minds. In other words, there are two lines of progress in science, each correcting the excesses of the other; both are essential if science is not to lose its way. The intuitive mind (and we are talking here chiefly of the formal-intuitive mind) is the mentality that allows for definite discovery; it is what keeps us grounded in reality. It calls us back to common sense, and provides the general background principles for rational discussion. Its two great characteristics are clarity and good sense. When the intuitive mind adds something to science, the addition illuminates. It articulates an explanation that makes sense because it is clearly linked to the principles rational human beings have in common. The geometrical mind, on the other hand, is the mentality that is deductive, rigorous, and precise. It follows reasoning wherever it goes. It is disciplined and patient in a way the intuitive mind is not. Whereas the intuitive mind is often the source of a new scientific discipline, it is the geometrical mind that takes the principles provided by the intuitive mind and sets them into a rigorous logical or mathematical order so that their consequences can be followed to the very end.

Duhem's constant worry throughout German Science is the imperialism of the geometrical mind. The geometrical mind is very rigorous and logical; but in another sense it is very unruly. The geometrical mind is impressed by reasoning as such; it is careless about the starting points of the deduction. Indeed, these are treated as almost insignificant; the geometrical mind just posits whatever starting points are convenient for whatever it is doing. There is no absolute problem with this; but there is the danger that the geometrical mind, carried away with following out a line of reasoning to its bitter end, will stifle or completely ignore the intuitive mind. It is the intuitive mind, remember, that keeps reasoning grounded in reality; it is also the intuitive mind that has the real skill to recognize when our reasoning has brought us to a genuine absurdity. Duhem's worry is that science is in danger of being highjacked by the geometrical mind's tendency to be seduced by sophisticated reasoning, thus losing sight of the reality it is really supposed to be explaining.

Nonetheless, even when the geometrical mind gets carried away, it is making genuine contributions to the progress of science. It is only if the intuitive mind is pushed out that we have serious problems. So for Duhem, a step forward in the progress of science can be a step forward either by the intuitive mind or by the geometrical mind. Duhem considers the theory of relativity to be a useful step forward along the geometrical line of progress. It tells us how you can go about preserving Maxwell's equations in the face of a number of perplexities; it allows us to make precise and accurate predictions we could not otherwise make. There is no question that Duhem considers this to be a valuable step forward.

However, what Duhem wants, and what he's not getting, is for the geometrical mind to allow the formal-intuitive mind to look at the theory of relativity and say, "OK, use it insofar as it is useful. But notice that we come up with several conclusions down the road that seem counterintuitive. Let's see if we can take what we've learned from the theory of relativity and go back to re-analyze the foundations from which it set out, in order to see if we can develop a theory that does not have these counterintuitive conclusions but preserves much of what is valuable about the theory of relativity. If we can find such a theory, that would be even better than the theory of relativity." Clearly, we can be wrong about the general principles of good sense or common sense, and sometimes have been (just as we have sometimes been wrong about the value for physics of this or that mathematical deduction); but Duhem finds it worrisome that so many people are willing to say, "By positing this starting point (the principles that will maintain the form of Maxwell's equations) and rigorously following our deductions through to useful effect, we have proven that such-and-such common-sense principle is false."

He recognizes that there is a practical value in the particular posited starting-point of the theory of relativity, and that the theory of relativity has numerous other practical values that show that it is, indeed, a major contribution to scientific progress: beauty, simplicity, predictive power. But it is the geometrical mind that is interested in these pragmatic values in the first place. The geometrical mind is interested in what you can do with scientific theories; it is interested in how they can facilitate the deductive processes so central to its approach. The formal-intuitive mind, however, is much less interested in pragmatic values like the beauty, simplicity, and predictive power of the theory. The formal-intuitive mind is not so much interested in what you can do with the theory, but in what it illuminates. The epistemological goal of the formal-intuitive mind is not a pragmatically valuable theory; it is instead a theory that makes things clear and obvious. The geometrical mind likes that you can use the theory of relativity to calculate satellite orbits; thinking in terms of clocks and rubber sheets and elevators might perhaps enchant the imaginative-intuitive mind for a while; but in Duhem's view the formal-intuitive mind is left in the dark if it is not allowed to use the theory of relativity to progress along its own line of interest. The formal-intuitive mind can accept the theory of relativity as a valuable contribution of the geometrical mind, but only on its own terms, which require using what we learn from it in order to find a theory that is either common-sensical or capable of becoming common-sensical when seen in the right way. Duhem is worried about the tendency of the geometrical mind to try to shut this down entirely. This heedlessness, this refusal even to take into account the fact that not all minds can be satisfied with what satisfies the geometrical mind, is Duhem's real irritation when it comes to the theory of relativity -- it is not the theory itself, but the refusal to recognize even the existence of the formal-intuitive mind and its needs. It is only in the cooperation of the geometrical and the intuitive minds that ideal science exists (German Science, p. 110):

French science, German science, both deviate from ideal and perfect science, but they deviate in two opposite ways. The one possesses excessively that with which the other is meagerly provided. In the one, the mathematical mind reduces the intuitive mind to the point of suffocation. In the other, the intuitive mind dispenses too readily with the mathematical mind.

Science needs the geometrical mind for rigor; but it needs the intuitive mind for truth. Such is Duhem's view, anyway. As he insists, "For science to be true, it is not sufficient that it be rigorous; it must start from good sense, only in order to return to good sense" (p. 111). It's not that he thinks the theory of relativity is bad science; what he objects to is the way he thinks that it has been co-opted by the 'German mind' in an attempt to present itself as the only way of looking at the world.---

All quotations from Pierre Duhem, German Science, John Lyon, tr. Open Court (La Salle, Illinois: 1991).

Tuesday, September 22, 2009

You have to love the Onion. (I remember an Onion headline that summed up for me much of the health care dispute: something like, Congress Deadlocked on How Best to Deny Health Care to the Poor.) What the Jags need to do, of course, is to recognize, perhaps by reading Simone de Beauvoir, that a distinction can be made between absurdity and ambiguity, and that what they are interpreting as the absurdity of human life is really the ambiguity of human existence, which allows for the creation of meaning through projects of freedom.

Disputes with men, pertinaciously obstinate in their principles, are, of all others, the most irksome; except, perhaps, those with persons a entirely disingenuous, who really do not believe the opinions they defend, but engage in the controversy from affectation, from a spirit of opposition, or from a desire of showing wit and ingenuity superior to the rest of mankind. The same blind adherence to their own arguments is to be expected in both; the same contempt of their antagonists; and the same passionate vehemence, in inforcing sophistry and falsehood. And as reasoning is not the source, whence either disputant derives his tenets; it is in vain to expect, that any logic, which speaks not to the affections, will ever engage him to embrace sounder principles.

Those who have denied the reality of moral distinctions, may be ranked among the disingenuous disputants; nor is it conceivable, that any human creature could ever seriously believe, that all characters and actions were alike entitled to the affection and regard of every one. The difference, which nature has placed between one man and another, is so wide, and this difference is still so much farther widened, by education, example, and habit, that, where the opposite extremes come at once under our apprehension, there is no scepticism so scrupulous, and scarce any assurance so determined, as absolutely to deny all distinction between them. Let a man's insensibility be ever so great, he must often be touched with the images of RIGHT and WRONG; and let his prejudices be ever so obstinate, he must observe, that others are susceptible of like impressions. The only way, therefore, of converting an antagonist of this kind, is to leave him to himself. For, finding that no body keeps up the controversy with him, it is probable he will, at last, of himself, from mere weariness, come over to the side of common sense and reason.

Monday, September 21, 2009

As is well known, one of the concepts that Kant uses to elucidate the categorical imperative is the kingdom of ends -- indeed, many people find it the most striking way of putting the matter, and you can find traces of the Kantian notion of priceless human dignity within a kingdom of ends in a great many places. One thing that's often overlooked, although it has been recognized by scholars of Kant, is that this notion is at its root a rationalist notion, and that Kant is essentially appropriating for his own, non-rationalist, purposes a notion that is found in the Leibnizian family of philosophical systems that Kant often takes to be paradigmatically rationalist.

Leibniz regards all spirits or minds as monads, each of which is distinct from the others, none of which actually interact, and each of which nonetheless runs in a pre-established harmony with all the others because each monad contains within itself all the truths about its relations to every other monad. Every monad, as Leibniz puts it, expresses God and the universe. Minds are not the only monads, in Leibniz's view; but they are the monads that are most clearly expressive of God and the universe, such that each mind-monad can be considered the image of God, vastly more valuable than anything else. All of these mind-monads are organized by their harmony with God into a moral realm, a City of God, a kingdom of grace. Within this kingdom of grace each monad acts with freedom; these expressions of freedom, however, are found in a harmony that has existed from all eternity due to God's selecting out from all possible world-lines that one that allows the greatest happiness of each that is consistent with the greatest harmony of all.

Kant builds on this in his account of the kingdom of ends. Each person or rational being is an end, capable of legislating himself under moral law; this moral law each person has in himself as a precondition of his very rationality. Because of this it is possible to think of all people together as being a unified whole, a systematic union of ends operating under a common moral law. Each person, however, operates with a sort of sovereign autonomy. Kant clearly links this to the Leibnizian City of God in the Mrongovius lecture notes from 1785 (29:610-611):

Man must regard himself as a legislating member of the kingdom of ends, or of rational beings. Leibnitz also calls the kingdom of ends moral principles of the kingdom of grace.

Thus we can think of Kant's kingdom of ends as a sort of ethical monadology, and the Kantian person as an autonomous legislator analogous to a Leibnizian monad.

This is all quite deliberate on Kant's part: as is often the case with Kantian philosophy, a great deal of the motive behind this appropriation is to capture what Kant likes in Wolff's mix of Leibniz and scholasticism, but also to de-fang it, to tear down its pretensions. We see this here. For despite the fact that Kant is appropriating Leibniz's monadic kingdom of grace, he is in a sense not affirming it. This is a very common tactic Kant uses against rationalism: what the rationalist takes categorically, Kant takes hypothetically. And in the process of outlining the kingdom of ends in his Groundwork, he takes the trouble to make the parenthetical comment that the kingdom of ends is "surely only an ideal." In this brief parenthetical aside is all the difference between Kant and Leibniz on this point. Leibniz's City of God is not an ideal; it is put forward as the way that God has really arranged the moral world. But Kant's kingdom of ends describes nothing real: it is merely an ideal we will as best we may, and a sort of analogy by which we understand the categorical imperative at the root of practical reason.

Caveats

For a rough introduction to my philosophy of blogging, including the Code of Amiability I try to follow on this weblog, please read my fifth anniversary post. I consider blogging to be a very informal type of publishing - like putting up thoughts on your door with a note asking for comments. Nothing in this weblog is done rigorously: it's a forum to let my mind be unruly, a place for jottings and first impressions. Because I consider posts here to be 'literary seedings' rather than finished products, nothing here should be taken as if it were anything more than an attempt to rough out some basic thoughts on various issues. Learning to look at any topic philosophically requires, I think, jumping right in, even knowing that you might be making a fool of yourelf; so that's what I do. My primary interest in most topics is the flow and structure of reasoning they involve rather than their actual conclusions, so most of my posts are about that. If, however, you find me making a clear factual error, let me know; blogging is a great way to get rid of misconceptions.